Least Common Multiple (LCM) of 119 and 137
The least common multiple (LCM) of 119 and 137 is 16303.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 119 and 137?
First, calculate the GCD of 119 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 137 = 0 remainder 119 |
| 2 | 137 ÷ 119 = 1 remainder 18 |
| 3 | 119 ÷ 18 = 6 remainder 11 |
| 4 | 18 ÷ 11 = 1 remainder 7 |
| 5 | 11 ÷ 7 = 1 remainder 4 |
| 6 | 7 ÷ 4 = 1 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 70 and 59 | 4130 |
| 131 and 148 | 19388 |
| 179 and 21 | 3759 |
| 32 and 10 | 160 |
| 101 and 84 | 8484 |